> If you're looking for concurrent code that doesn't use `unsafe` you won't find any.
The Rust standard library provides a bunch of concurrency primitives. You can write 100% safe Rust code use these primitives to do things concurrently, and Rust guarantees that your resulting program is free of a specific category of bugs: memory errors, data races, etc. No other mainstream language gives you this combination of concurrency safety and efficiency.
The implementation of the concurrency primitives, however, often includes assembly, or C, or unsafe Rust code, which the Rust compiler can't provide guarantees for. We have to rely on humans for that. This is the norm for almost all programming languages.
Ideally, yes, it would be nice if the safe subset of Rust were powerful enough to implement efficient concurrency primitives, but that would add a TON of complexity to the type system.
People are generally ok with the Rust standard library using assembly, C, or unsafe Rust, because even though it can be tricky to write this kind of code correctly, the standard library is maintained by Rust experts who take every change seriously.
People tend to worry more about third party libraries because, on average, the authors are not Rust language experts and may not understand the subtleties.